Chapter 6eng.staff.alexu.edu.eg/~mmorsy/Courses/.../PDFs/Lectures/DDCA_Ch6.pdfPhysics Devices Analog Circuits Digital Circuits Logic ... • President of Stanford University ... Chapter

Chapter 6 <1>

Digital Design and Computer Architecture, 2nd Edition

Chapter 6

David Money Harris and Sarah L. Harris

Chapter 6 <2>

Chapter 6 :: Topics

• Introduction

• Assembly Language

• Machine Language

• Programming

• Addressing Modes

• Lights, Camera, Action: Compiling, Assembling, & Loading

• Odds and Ends

Chapter 6 <3>

• Jumping up a few levels of abstraction

• Architecture:programmer’s view of computer– Defined by instructions &

operand locations

• Microarchitecture: how to implement an architecture in hardware (covered in Chapter 7)

Physics

Devices

Analog

Circuits

Digital

Circuits

Logic

Micro-

architecture

Architecture

Operating

Systems

Application

Software

electrons

transistors

diodes

amplifiers

filters

AND gates

NOT gates

adders

memories

datapaths

controllers

instructions

registers

device drivers

programs

Introduction

Chapter 6 <4>

• Instructions: commands in a computer’s language– Assembly language: human-readable format of

instructions– Machine language: computer-readable format

(1’s and 0’s)

• MIPS architecture:– Developed by John Hennessy and his colleagues at

Stanford and in the 1980’s.– Used in many commercial systems, including

Silicon Graphics, Nintendo, and Cisco

Once you’ve learned one architecture, it’s easy to learn others

Assembly Language

Chapter 6 <5>

• President of Stanford University

• Professor of Electrical Engineering and Computer Science at Stanford since 1977

• Coinvented the Reduced Instruction Set Computer (RISC) with David Patterson

• Developed the MIPS architecture at Stanford in 1984 and cofounded MIPS Computer Systems

• As of 2004, over 300 million MIPS microprocessors have been sold

John Hennessy

Chapter 6 <6>

Underlying design principles, as articulated by Hennessy and Patterson:

1.Simplicity favors regularity

2.Make the common case fast

3.Smaller is faster

4.Good design demands good compromises

Architecture Design Principles

Chapter 6 <7>

• add: mnemonic indicates operation to perform

• b, c: source operands (on which the operation is performed)

• a: destination operand (to which the result is written)

C Code

a = b + c;

MIPS assembly code

add a, b, c

Instructions: Addition

Chapter 6 <8>

• Similar to addition - only mnemonic changes

• sub: mnemonic

• b, c: source operands

• a: destination operand

C Code

a = b - c;

MIPS assembly code

sub a, b, c

Instructions: Subtraction

Chapter 6 <9>

Simplicity favors regularity

• Consistent instruction format

• Same number of operands (two sources and one destination)

• easier to encode and handle in hardware

Design Principle 1

Chapter 6 <10>

• More complex code is handled by multiple MIPS instructions.

C Code

a = b + c - d;

MIPS assembly code

add t, b, c # t = b + c

sub a, t, d # a = t - d

Multiple Instructions

Chapter 6 <11>

Make the common case fast• MIPS includes only simple, commonly used instructions

• Hardware to decode and execute instructions can be simple, small, and fast

• More complex instructions (that are less common) performed using multiple simple instructions

• MIPS is a reduced instruction set computer (RISC), with a small number of simple instructions

• Other architectures, such as Intel’s x86, are complex instruction set computers (CISC)

Design Principle 2

Chapter 6 <12>

• Operand location: physical location in computer

– Registers

– Memory

– Constants (also called immediates)

Operands

Chapter 6 <13>

• MIPS has 32 32-bit registers

• Registers are faster than memory

• MIPS called “32-bit architecture” because it operates on 32-bit data

Operands: Registers

Chapter 6 <14>

Smaller is Faster

• MIPS includes only a small number of registers

Design Principle 3

Chapter 6 <15>

Name Register Number Usage

$0 0 the constant value 0

$at 1 assembler temporary

$v0-$v1 2-3 Function return values

$a0-$a3 4-7 Function arguments

$t0-$t7 8-15 temporaries

$s0-$s7 16-23 saved variables

$t8-$t9 24-25 more temporaries

$k0-$k1 26-27 OS temporaries

$gp 28 global pointer

$sp 29 stack pointer

$fp 30 frame pointer

$ra 31 Function return address

MIPS Register Set

Chapter 6 <16>

• Registers:– $ before name

– Example: $0, “register zero”, “dollar zero”

• Registers used for specific purposes: • $0 always holds the constant value 0.

• the saved registers, $s0-$s7, used to hold variables

• the temporary registers, $t0 - $t9, used to hold intermediate values during a larger computation

• Discuss others later

Operands: Registers

Chapter 6 <17>

• Revisit add instruction

C Code

a = b + c

MIPS assembly code

# $s0 = a, $s1 = b, $s2 = c

add $s0, $s1, $s2

Instructions with Registers

Chapter 6 <18>

• Too much data to fit in only 32 registers

• Store more data in memory

• Memory is large, but slow

• Commonly used variables kept in registers

Operands: Memory

Chapter 6 <19>

Data

00000003 4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

00000002

00000001

00000000

Word Address

Word 3

Word 2

Word 1

Word 0

• Each 32-bit data word has a unique address

Word-Addressable Memory

Chapter 6 <20>

• Memory read called load

• Mnemonic: load word (lw)

• Format:

lw $s0, 5($t1)

• Address calculation:– add base address ($t1) to the offset (5)

– address = ($t1 + 5)

• Result:– $s0 holds the value at address ($t1 + 5)

Any register may be used as base address

Reading Word-Addressable Memory

Chapter 6 <21>

Data

00000003 4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

00000002

00000001

00000000

Word Address

Word 3

Word 2

Word 1

Word 0

• Example: read a word of data at memory address 1 into $s3– address = ($0 + 1) = 1

– $s3 = 0xF2F1AC07 after load

Assembly code

lw $s3, 1($0) # read memory word 1 into $s3

Reading Word-Addressable Memory

Chapter 6 <22>

• Memory write are called store

• Mnemonic: store word (sw)

Writing Word-Addressable Memory

Chapter 6 <23>

Data

00000003 4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

00000002

00000001

00000000

Word Address

Word 3

Word 2

Word 1

Word 0

• Example: Write (store) the value in $t4into memory address 7 – add the base address ($0) to the offset (0x7)

– address: ($0 + 0x7) = 7

Offset can be written in decimal (default) or hexadecimal

Assembly code

sw $t4, 0x7($0) # write the value in $t4

# to memory word 7

Writing Word-Addressable Memory

Chapter 6 <24>

Word Address Data

0000000C

00000008

00000004

00000000

width = 4 bytes

4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

Word 3

Word 2

Word 1

Word 0

• Each data byte has unique address

• Load/store words or single bytes: load byte (lb) and store byte (sb)

• 32-bit word = 4 bytes, so word address increments by 4

Byte-Addressable Memory

Chapter 6 <25>

• The address of a memory word must now be multiplied by 4. For example,– the address of memory word 2 is 2 × 4 = 8

– the address of memory word 10 is 10 × 4 = 40 (0x28)

• MIPS is byte-addressed, not word-addressed

Reading Byte-Addressable Memory

Chapter 6 <26>

Word Address Data

0000000C

00000008

00000004

00000000

width = 4 bytes

4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

Word 3

Word 2

Word 1

Word 0

• Example: Load a word of data at memory address 4 into $s3.

• $s3 holds the value 0xF2F1AC07 after load

MIPS assembly code

lw $s3, 4($0) # read word at address 4 into $s3

Reading Byte-Addressable Memory

Chapter 6 <27>

Word Address Data

0000000C

00000008

00000004

00000000

width = 4 bytes

4 0 F 3 0 7 8 8

0 1 E E 2 8 4 2

F 2 F 1 A C 0 7

A B C D E F 7 8

Word 3

Word 2

Word 1

Word 0

• Example: stores the value held in $t7into memory address 0x2C (44)

MIPS assembly code

sw $t7, 44($0) # write $t7 into address 44

Writing Byte-Addressable Memory

Chapter 6 <28>

0 1 2 3

MSB LSB

4 5 6 7

8 9 A B

C D E F

Byte

Address

3 2 1 00

7 6 5 44

B A 9 88

F E D CC

Byte

Address

Word

Address

Big-Endian Little-Endian

MSB LSB

• How to number bytes within a word?

• Little-endian: byte numbers start at the little (least significant) end

• Big-endian: byte numbers start at the big (most significant) end

• Word address is the same for big- or little-endian

Big-Endian & Little-Endian Memory

Chapter 6 <29>

0 1 2 3

MSB LSB

4 5 6 7

8 9 A B

C D E F

Byte

Address

3 2 1 00

7 6 5 44

B A 9 88

F E D CC

Byte

Address

Word

Address


MSB LSB

• Jonathan Swift’s Gulliver’s Travels: the Little-Endiansbroke their eggs on the little end of the egg and the Big-Endians broke their eggs on the big end

• It doesn’t really matter which addressing type used –except when the two systems need to share data!

Big-Endian & Little-Endian Memory

Chapter 6 <30>

• Suppose $t0 initially contains 0x23456789

• After following code runs on big-endian system, what

value is $s0?

• In a little-endian system?

sw $t0, 0($0)

lb $s0, 1($0)

Big-Endian & Little-Endian Example

Chapter 6 <31>

• Suppose $t0 initially contains 0x23456789

• After following code runs on big-endian system, what

value is $s0?

• In a little-endian system?

sw $t0, 0($0)

lb $s0, 1($0)

• Big-endian: 0x00000045

• Little-endian: 0x00000067

Big-Endian & Little-Endian Example

23 45 67 89

0 1 2 3

23 45 67 890

3 2 1 0Word

Address


Byte Address

Data Value

Byte Address

Data Value

MSB LSB MSB LSB

Chapter 6 <32>

Good design demands good compromises

• Multiple instruction formats allow flexibility- add, sub: use 3 register operands

- lw, sw: use 2 register operands and a constant

• Number of instruction formats kept small

- to adhere to design principles 1 and 3 (simplicity favors regularity and smaller is faster).

Design Principle 4

Chapter 6 <33>

• lw and sw use constants or immediates

• immediately available from instruction

• 16-bit two’s complement number

• addi: add immediate

• Subtract immediate (subi) necessary?

C Code

a = a + 4;

b = a – 12;

MIPS assembly code

# $s0 = a, $s1 = b

addi $s0, $s0, 4

addi $s1, $s0, -12

Operands: Constants/Immediates

Chapter 6 <34>

• Binary representation of instructions

• Computers only understand 1’s and 0’s

• 32-bit instructions – Simplicity favors regularity: 32-bit data &

instructions

• 3 instruction formats:– R-Type: register operands

– I-Type: immediate operand

– J-Type: for jumping (discuss later)

Machine Language

Chapter 6 <35>

op rs rt rd shamt funct

6 bits 5 bits 5 bits 5 bits 5 bits 6 bits

R-Type

• Register-type

• 3 register operands:– rs, rt: source registers

– rd: destination register

• Other fields:– op: the operation code or opcode (0 for R-type instructions)

– funct: the function

with opcode, tells computer what operation to perform

– shamt: the shift amount for shift instructions, otherwise it’s 0

R-Type

Chapter 6 <36>

add $s0, $s1, $s2

sub $t0, $t3, $t5

Assembly Code

0 17 18 16 0 32

Field Values

0 11 13 8 0 34



000000 10001 10010 10000 00000 100000


000000 01011 01101 01000 00000 100010

Machine Code


(0x02328020)

(0x016D4022)

Note the order of registers in the assembly code:

add rd, rs, rt

R-Type Examples

Chapter 6 <37>

op rs rt imm

6 bits 5 bits 5 bits 16 bits

I-Type

• Immediate-type

• 3 operands:– rs, rt: register operands

– imm: 16-bit two’s complement immediate

• Other fields:– op: the opcode

– Simplicity favors regularity: all instructions have opcode

– Operation is completely determined by opcode

I-Type

Chapter 6 <38>

Assembly Code

8 17 16 5

Field Valuesop rs rt imm


addi $s0, $s1, 5

addi $t0, $s3, -12

lw $t2, 32($0)

sw $s1, 4($t1)

8 19 8 -12

35 0 10 32

43 9 17 4

(0x22300005)

(0x2268FFF4)

(0x8C0A0020)

(0xAD310004)

001000 10001 10000 0000 0000 0000 0101

op rs rt imm

Machine Code


001000 10011 01000 1111 1111 1111 0100

100011 00000 01010 0000 0000 0010 0000

101011 01001 10001 0000 0000 0000 0100

Note the differing order of

registers in assembly and

machine codes:

addi rt, rs, imm

lw rt, imm(rs)

sw rt, imm(rs)

I-Type Examples

Chapter 6 <39>

op addr

6 bits 26 bits

J-Type

• Jump-type

• 26-bit address operand (addr)

• Used for jump instructions (j)

Machine Language: J-Type

Chapter 6 <40>



R-Type

op rs rt imm


I-Type

op addr

6 bits 26 bits

J-Type

Review: Instruction Formats

Chapter 6 <41>

• 32-bit instructions & data stored in memory

• Sequence of instructions: only difference between two applications

• To run a new program:– No rewiring required

– Simply store new program in memory

• Program Execution:– Processor fetches (reads) instructions from memory

in sequence

– Processor performs the specified operation

Power of the Stored Program

Chapter 6 <42>

addi $t0, $s3, -12

Machine CodeAssembly Code

lw $t2, 32($0)

add $s0, $s1, $s2

sub $t0, $t3, $t5

0x8C0A0020

0x02328020

0x2268FFF4

0x016D4022

Address Instructions

0040000C 0 1 6 D 4 0 2 2

2 2 6 8 F F F 4

0 2 3 2 8 0 2 0

8 C 0 A 0 0 2 0

00400008

00400004

00400000

Stored Program

Main Memory

PC

The Stored Program

Program Counter (PC): keeps track of current instruction

Chapter 6 <43>

001000 10001 10111 1111 1111 1111 0001

op rs rt imm

addi $s7, $s1, -15

Machine Code Assembly Code

8 17 23 -15

Field Values

(0x2237FFF1)

op rs rt imm

2 2 3 7 F F F 1

000000 10111 10011 01000 00000 100010


sub $t0, $s7, $s3 0 23 19 8 0 34(0x02F34022)


0 2 F 3 4 0 2 2

• Start with opcode: tells how to parse rest

• If opcode all 0’s– R-type instruction

– Function bits tell operation

• Otherwise– opcode tells operation

Interpreting Machine Code

Chapter 6 <44>

• High-level languages: – e.g., C, Java, Python

– Written at higher level of abstraction

• Common high-level software constructs:– if/else statements

– for loops

– while loops

– arrays

– function calls

Programming

Chapter 6 <45>

• Wrote the first computer program

• Her program calculated the Bernoulli numbers on Charles Babbage’s Analytical Engine

• She was the only legitimate child of the poet Lord Byron

Ada Lovelace, 1815-1852

Chapter 6 <46>

• and, or, xor, nor– and: useful for masking bits

• Masking all but the least significant byte of a value:

0xF234012F AND 0x000000FF = 0x0000002F

– or: useful for combining bit fields

• Combine 0xF2340000 with 0x000012BC:

0xF2340000 OR 0x000012BC = 0xF23412BC

– nor: useful for inverting bits:

• A NOR $0 = NOT A

• andi, ori, xori– 16-bit immediate is zero-extended (not sign-extended)

– nori not needed

Logical Instructions

Chapter 6 <47>

1111 1111 1111 1111 0000 0000 0000 0000$s1

0100 0110 1010 0001 1111 0000 1011 0111$s2

$s3

$s4

$s5

$s6

Source Registers

ResultAssembly Code

and $s3, $s1, $s2

or $s4, $s1, $s2

xor $s5, $s1, $s2

nor $s6, $s1, $s2

Logical Instructions Example 1

Chapter 6 <48>

1111 1111 1111 1111 0000 0000 0000 0000$s1

0100 0110 1010 0001 1111 0000 1011 0111$s2

0100 0110 1010 0001 0000 0000 0000 0000$s3

1111 1111 1111 1111 1111 0000 1011 0111$s4

1011 1001 0101 1110 1111 0000 1011 0111$s5

0000 0000 0000 0000 0000 1111 0100 1000$s6

Source Registers

ResultAssembly Code

and $s3, $s1, $s2

or $s4, $s1, $s2

xor $s5, $s1, $s2

nor $s6, $s1, $s2


Chapter 6 <49>

0000 0000 0000 0000 0000 0000 1111 1111$s1

Assembly Code

0000 0000 0000 0000 1111 1010 0011 0100imm

$s2

$s3

$s4

andi $s2, $s1, 0xFA34

Source Values

Result

ori $s3, $s1, 0xFA34

xori $s4, $s1, 0xFA34

zero-extended


Chapter 6 <50>

0000 0000 0000 0000 0000 0000 1111 1111$s1

Assembly Code

0000 0000 0000 0000 1111 1010 0011 0100imm

0000 0000 0000 0000 0000 0000 0011 0100$s2

0000 0000 0000 0000 1111 1010 1111 1111$s3

0000 0000 0000 0000 1111 1010 1100 1011$s4

andi $s2, $s1, 0xFA34

Source Values

Result

ori $s3, $s1, 0xFA34

xori $s4, $s1, 0xFA34

zero-extended


Chapter 6 <51>

• sll: shift left logical– Example: sll $t0, $t1, 5 # $t0 <= $t1 << 5

• srl: shift right logical– Example: srl $t0, $t1, 5 # $t0 <= $t1 >> 5

• sra: shift right arithmetic– Example: sra $t0, $t1, 5 # $t0 <= $t1 >>> 5

Shift Instructions

Chapter 6 <52>

• sllv: shift left logical variable– Example: sllv $t0, $t1, $t2 # $t0 <= $t1 << $t2

• srlv: shift right logical variable– Example: srlv $t0, $t1, $t2 # $t0 <= $t1 >> $t2

• srav: shift right arithmetic variable– Example: srav $t0, $t1, $t2 # $t0 <= $t1 >>> $t2

Variable Shift Instructions

Chapter 6 <53>

sll $t0, $s1, 2

srl $s2, $s1, 2

sra $s3, $s1, 2

Assembly Code

0 0 17 8 2 0

Field Valuesop rs rt rd shamt funct


0 0 17 18 2 2

0 0 17 19 2 3

000000 00000 10001 01000 00010 000000


Machine Code


000000 00000 10001 10010 00010 000010

000000 00000 10001 10011 00010 000011

(0x00114080)

(0x00119082)

(0x00119883)

Shift Instructions

Chapter 6 <54>

• 16-bit constants using addi:

• 32-bit constants using load upper immediate (lui) and ori:

C Code

int a = 0xFEDC8765;

MIPS assembly code

# $s0 = a

lui $s0, 0xFEDC

ori $s0, $s0, 0x8765

C Code

// int is a 32-bit signed word

int a = 0x4f3c;

MIPS assembly code

# $s0 = a

addi $s0, $0, 0x4f3c

Generating Constants

Chapter 6 <55>

• Special registers: lo, hi

• 32 × 32 multiplication, 64 bit result– mult $s0, $s1

– Result in {hi, lo}

• 32-bit division, 32-bit quotient, remainder– div $s0, $s1

– Quotient in lo

– Remainder in hi

• Moves from lo/hi special registers– mflo $s2

– mfhi $s3

Multiplication, Division

Chapter 6 <56>

• Execute instructions out of sequence

• Types of branches:

– Conditional• branch if equal (beq)

• branch if not equal (bne)

– Unconditional• jump (j)

• jump register (jr)

• jump and link (jal)

Branching

Chapter 6 <57>

addi $t0, $s3, -12

Machine CodeAssembly Code

lw $t2, 32($0)

add $s0, $s1, $s2

sub $t0, $t3, $t5

0x8C0A0020

0x02328020

0x2268FFF4

0x016D4022

Address Instructions

0040000C 0 1 6 D 4 0 2 2

2 2 6 8 F F F 4

0 2 3 2 8 0 2 0

8 C 0 A 0 0 2 0

00400008

00400004

00400000

Stored Program

Main Memory

PC

Review: The Stored Program

Chapter 6 <58>

# MIPS assemblyaddi $s0, $0, 4 # $s0 = 0 + 4 = 4

addi $s1, $0, 1 # $s1 = 0 + 1 = 1

sll $s1, $s1, 2 # $s1 = 1 << 2 = 4

beq $s0, $s1, target # branch is taken

addi $s1, $s1, 1 # not executed

sub $s1, $s1, $s0 # not executed

target: # label

add $s1, $s1, $s0 # $s1 = 4 + 4 = 8

Labels indicate instruction location. They can’t be reserved words and

must be followed by colon (:)

Conditional Branching (beq)

Chapter 6 <59>

# MIPS assemblyaddi $s0, $0, 4 # $s0 = 0 + 4 = 4

addi $s1, $0, 1 # $s1 = 0 + 1 = 1

sll $s1, $s1, 2 # $s1 = 1 << 2 = 4

bne $s0, $s1, target # branch not taken

addi $s1, $s1, 1 # $s1 = 4 + 1 = 5

sub $s1, $s1, $s0 # $s1 = 5 – 4 = 1

target:

add $s1, $s1, $s0 # $s1 = 1 + 4 = 5

The Branch Not Taken (bne)

Chapter 6 <60>

# MIPS assemblyaddi $s0, $0, 4 # $s0 = 4

addi $s1, $0, 1 # $s1 = 1

j target # jump to target

sra $s1, $s1, 2 # not executed

addi $s1, $s1, 1 # not executed

sub $s1, $s1, $s0 # not executed

target:

add $s1, $s1, $s0 # $s1 = 1 + 4 = 5

Unconditional Branching (j)

Chapter 6 <61>

# MIPS assembly

0x00002000 addi $s0, $0, 0x2010

0x00002004 jr $s0

0x00002008 addi $s1, $0, 1

0x0000200C sra $s1, $s1, 2

0x00002010 lw $s3, 44($s1)

jr is an R-type instruction.

Unconditional Branching (jr)

Chapter 6 <62>

• if statements

• if/else statements

• while loops

• for loops

High-Level Code Constructs

Chapter 6 <63>

C Code

if (i == j)

f = g + h;

f = f – i;

MIPS assembly code

# $s0 = f, $s1 = g, $s2 = h

# $s3 = i, $s4 = j

If Statement

Chapter 6 <64>

C Code

if (i == j)

f = g + h;

f = f – i;

MIPS assembly code

# $s0 = f, $s1 = g, $s2 = h

# $s3 = i, $s4 = j

bne $s3, $s4, L1

add $s0, $s1, $s2

L1: sub $s0, $s0, $s3

Assembly tests opposite case (i != j) of high-level code (i == j)

If Statement

Chapter 6 <65>

C Code

if (i == j)

f = g + h;

else

f = f – i;

MIPS assembly code

If/Else Statement

Chapter 6 <66>

C Code

if (i == j)

f = g + h;

else

f = f – i;

MIPS assembly code

# $s0 = f, $s1 = g, $s2 = h

# $s3 = i, $s4 = j

bne $s3, $s4, L1

add $s0, $s1, $s2

j done

L1: sub $s0, $s0, $s3

done:

If/Else Statement

Chapter 6 <67>

C Code// determines the power

// of x such that 2x = 128

int pow = 1;

int x = 0;

while (pow != 128) {

pow = pow * 2;

x = x + 1;

}

MIPS assembly code

Assembly tests for the opposite case (pow == 128) of the C code (pow != 128).

While Loops

Chapter 6 <68>

C Code// determines the power

// of x such that 2x = 128

int pow = 1;

int x = 0;

while (pow != 128) {

pow = pow * 2;

x = x + 1;

}

MIPS assembly code# $s0 = pow, $s1 = x

addi $s0, $0, 1

add $s1, $0, $0

addi $t0, $0, 128

while: beq $s0, $t0, done

sll $s0, $s0, 1

addi $s1, $s1, 1

j while

done:

Assembly tests for the opposite case (pow == 128) of the C code (pow != 128).

While Loops

Chapter 6 <69>

for (initialization; condition; loop operation)

statement

• initialization: executes before the loop begins

• condition: is tested at the beginning of each iteration

• loop operation: executes at the end of each iteration

• statement: executes each time the condition is met

For Loops

Chapter 6 <70>

High-level code// add the numbers from 0 to 9

int sum = 0;

int i;

for (i=0; i!=10; i = i+1) {

sum = sum + i;

}

MIPS assembly code# $s0 = i, $s1 = sum

For Loops

Chapter 6 <71>

C Code// add the numbers from 0 to 9

int sum = 0;

int i;

for (i=0; i!=10; i = i+1) {

sum = sum + i;

}

MIPS assembly code

For Loops

Chapter 6 <72>

C Code// add the numbers from 0 to 9

int sum = 0;

int i;

for (i=0; i!=10; i = i+1) {

sum = sum + i;

}


addi $s1, $0, 0

add $s0, $0, $0

addi $t0, $0, 10

for: beq $s0, $t0, done

add $s1, $s1, $s0

addi $s0, $s0, 1

j for

done:

For Loops

Chapter 6 <73>

C Code// add the powers of 2 from 1

// to 100

int sum = 0;

int i;

for (i=1; i < 101; i = i*2) {

sum = sum + i;

}

MIPS assembly code

Less Than Comparison

Chapter 6 <74>

C Code// add the powers of 2 from 1

// to 100

int sum = 0;

int i;

for (i=1; i < 101; i = i*2) {

sum = sum + i;

}


addi $s1, $0, 0

addi $s0, $0, 1

addi $t0, $0, 101

loop: slt $t1, $s0, $t0

beq $t1, $0, done

add $s1, $s1, $s0

sll $s0, $s0, 1

j loop

done:

$t1 = 1 if i < 101

Less Than Comparison

Chapter 6 <75>

• Access large amounts of similar data

• Index: access each element

• Size: number of elements

Arrays

Chapter 6 <76>

array[4]

array[3]

array[2]

array[1]

array[0]0x12348000

0x12348004

0x12348008

0x1234800C

0x12340010

• 5-element array

• Base address = 0x12348000 (address of first element,

array[0])

• First step in accessing an array: load base address into a

register

Arrays

Chapter 6 <77>

// C Code

int array[5];

array[0] = array[0] * 2;


Accessing Arrays

Chapter 6 <78>

// C Code

int array[5];



# MIPS assembly code

# array base address = $s0

lui $s0, 0x1234 # 0x1234 in upper half of $S0

ori $s0, $s0, 0x8000 # 0x8000 in lower half of $s0

lw $t1, 0($s0) # $t1 = array[0]

sll $t1, $t1, 1 # $t1 = $t1 * 2

sw $t1, 0($s0) # array[0] = $t1

lw $t1, 4($s0) # $t1 = array[1]

sll $t1, $t1, 1 # $t1 = $t1 * 2

sw $t1, 4($s0) # array[1] = $t1

Accessing Arrays

Chapter 6 <79>

// C Code

int array[1000];

int i;

for (i=0; i < 1000; i = i + 1)

array[i] = array[i] * 8;


# $s0 = array base address, $s1 = i

Arrays using For Loops

Chapter 6 <80>


# $s0 = array base address, $s1 = i

# initialization code

lui $s0, 0x23B8 # $s0 = 0x23B80000

ori $s0, $s0, 0xF000 # $s0 = 0x23B8F000

addi $s1, $0, 0 # i = 0

addi $t2, $0, 1000 # $t2 = 1000

loop:

slt $t0, $s1, $t2 # i < 1000?

beq $t0, $0, done # if not then done

sll $t0, $s1, 2 # $t0 = i * 4 (byte offset)

add $t0, $t0, $s0 # address of array[i]

lw $t1, 0($t0) # $t1 = array[i]

sll $t1, $t1, 3 # $t1 = array[i] * 8

sw $t1, 0($t0) # array[i] = array[i] * 8

addi $s1, $s1, 1 # i = i + 1

j loop # repeat

done:

Arrays Using For Loops

Chapter 6 <81>

• American Standard Code for Information Interchange

• Each text character has unique byte value– For example, S = 0x53, a = 0x61, A = 0x41

– Lower-case and upper-case differ by 0x20 (32)

ASCII Code

Chapter 6 <82>

Cast of Characters

Chapter 6 <83>

• Caller: calling function (in this case, main)

• Callee: called function (in this case, sum)

C Codevoid main()

{

int y;

y = sum(42, 7);

...

}

int sum(int a, int b)

{

return (a + b);

}

Function Calls

Chapter 6 <84>

• Caller:– passes arguments to callee

– jumps to callee

• Callee: – performs the function

– returns result to caller

– returns to point of call

– must not overwrite registers or memory needed by caller

Function Conventions

Chapter 6 <85>

• Call Function: jump and link (jal)

• Return from function: jump register (jr)

• Arguments: $a0 - $a3

• Return value: $v0

MIPS Function Conventions

Chapter 6 <86>

C Codeint main() {

simple();

a = b + c;

}

void simple() {

return;

}

MIPS assembly code

0x00400200 main: jal simple

0x00400204 add $s0, $s1, $s2

...

0x00401020 simple: jr $ra

void means that simple doesn’t return a value

Function Calls

Chapter 6 <87>

C Codeint main() {

simple();

a = b + c;

}

void simple() {

return;

}

MIPS assembly code

0x00400200 main: jal simple

0x00400204 add $s0, $s1, $s2

...

0x00401020 simple: jr $ra

jal: jumps to simple

$ra = PC + 4 = 0x00400204

jr $ra: jumps to address in $ra (0x00400204)

Function Calls

Chapter 6 <88>

MIPS conventions:

• Argument values: $a0 - $a3

• Return value: $v0

Input Arguments & Return Value

Chapter 6 <89>

C Codeint main()

{

int y;

...

y = diffofsums(2, 3, 4, 5); // 4 arguments

...

}

int diffofsums(int f, int g, int h, int i)

{

int result;

result = (f + g) - (h + i);

return result; // return value

}


Chapter 6 <90>

MIPS assembly code# $s0 = y

main:

...

addi $a0, $0, 2 # argument 0 = 2




jal diffofsums # call Function

add $s0, $v0, $0 # y = returned value

...

# $s0 = result

diffofsums:

add $t0, $a0, $a1 # $t0 = f + g

add $t1, $a2, $a3 # $t1 = h + i

sub $s0, $t0, $t1 # result = (f + g) - (h + i)

add $v0, $s0, $0 # put return value in $v0

jr $ra # return to caller


Chapter 6 <91>

MIPS assembly code# $s0 = result

diffofsums:

add $t0, $a0, $a1 # $t0 = f + g

add $t1, $a2, $a3 # $t1 = h + i




• diffofsums overwrote 3 registers: $t0, $t1, $s0•diffofsums can use stack to temporarily store registers


Chapter 6 <92>

• Memory used to temporarily

save variables

• Like stack of dishes, last-in-

first-out (LIFO) queue

• Expands: uses more

memory when more space

needed

• Contracts: uses less

memory when the space is

no longer needed

The Stack

Chapter 6 <93>

Data

7FFFFFFC 12345678

7FFFFFF8

7FFFFFF4

7FFFFFF0

Address

$sp 7FFFFFFC

7FFFFFF8

7FFFFFF4

7FFFFFF0

Address Data

12345678

$sp

AABBCCDD

11223344

• Grows down (from higher to lower memory

addresses)

• Stack pointer: $sp points to top of the stack

The Stack

Chapter 6 <94>

# MIPS assembly

# $s0 = result

diffofsums:

add $t0, $a0, $a1 # $t0 = f + g

add $t1, $a2, $a3 # $t1 = h + i




• Called functions must have no unintended side

effects

• But diffofsums overwrites 3 registers: $t0,

$t1, $s0

How Functions use the Stack

Chapter 6 <95>

# $s0 = result

diffofsums:

addi $sp, $sp, -12 # make space on stack

# to store 3 registers

sw $s0, 8($sp) # save $s0 on stack

sw $t0, 4($sp) # save $t0 on stack

sw $t1, 0($sp) # save $t1 on stack

add $t0, $a0, $a1 # $t0 = f + g

add $t1, $a2, $a3 # $t1 = h + i



lw $t1, 0($sp) # restore $t1 from stack

lw $t0, 4($sp) # restore $t0 from stack

lw $s0, 8($sp) # restore $s0 from stack

addi $sp, $sp, 12 # deallocate stack space


Storing Register Values on the Stack

Chapter 6 <96>

Data

FC

F8

F4

F0

Address

$sp

(a)

Data

FC

F8

F4

F0

Address

$sp

(b)

$s0

Data

$sp

(c)

$t0

FC

F8

F4

F0

Address

? ??

sta

ck fra

me

$t1

The stack during diffofsums Call

Chapter 6 <97>

PreservedCallee-Saved

NonpreservedCaller-Saved

$s0-$s7 $t0-$t9

$ra $a0-$a3

$sp $v0-$v1

stack above $sp stack below $sp

Registers

Chapter 6 <98>

proc1:

addi $sp, $sp, -4 # make space on stack

sw $ra, 0($sp) # save $ra on stack

jal proc2

...

lw $ra, 0($sp) # restore $s0 from stack



Multiple Function Calls

Chapter 6 <99>

# $s0 = result

diffofsums:

addi $sp, $sp, -4 # make space on stack to

# store one register

sw $s0, 0($sp) # save $s0 on stack

# no need to save $t0 or $t1

add $t0, $a0, $a1 # $t0 = f + g

add $t1, $a2, $a3 # $t1 = h + i



lw $s0, 0($sp) # restore $s0 from stack



Storing Saved Registers on the Stack

Chapter 6 <100>

High-level codeint factorial(int n) {

if (n <= 1)

return 1;

else

return (n * factorial(n-1));

}

Recursive Function Call

Chapter 6 <101>

MIPS assembly code


Chapter 6 <102>

MIPS assembly code

0x90 factorial: addi $sp, $sp, -8 # make room

0x94 sw $a0, 4($sp) # store $a0

0x98 sw $ra, 0($sp) # store $ra

0x9C addi $t0, $0, 2

0xA0 slt $t0, $a0, $t0 # a <= 1 ?

0xA4 beq $t0, $0, else # no: go to else

0xA8 addi $v0, $0, 1 # yes: return 1

0xAC addi $sp, $sp, 8 # restore $sp

0xB0 jr $ra # return

0xB4 else: addi $a0, $a0, -1 # n = n - 1

0xB8 jal factorial # recursive call

0xBC lw $ra, 0($sp) # restore $ra

0xC0 lw $a0, 4($sp) # restore $a0

0xC4 addi $sp, $sp, 8 # restore $sp

0xC8 mul $v0, $a0, $v0 # n * factorial(n-1)

0xCC jr $ra # return


Chapter 6 <103>

$sp FC

F8

F4

F0

$ra

EC

E8

E4

E0

DC

FC

F8

F4

F0

EC

E8

E4

E0

DC

FC

F8

F4

F0

EC

E8

E4

E0

DC

$sp

$sp

$sp

$sp

$a0 = 1

$v0 = 1 x 1

$a0 = 2

$v0 = 2 x 1

$a0 = 3

$v0 = 3 x 2

$v0 = 6

$sp

$sp

$sp

$sp

DataAddress DataAddress DataAddress

$a0 (0x3)

$ra (0xBC)

$a0 (0x2)

$ra (0xBC)

$a0 (0x1)

$ra

$a0 (0x3)

$ra (0xBC)

$a0 (0x2)

$ra (0xBC)

$a0 (0x1)

Stack During Recursive Call

Chapter 6 <104>

• Caller– Put arguments in $a0-$a3

– Save any needed registers ($ra, maybe $t0-t9)

– jal callee

– Restore registers

– Look for result in $v0

• Callee– Save registers that might be disturbed ($s0-$s7)

– Perform function

– Put result in $v0

– Restore registers

– jr $ra

Function Call Summary

Chapter 6 <105>

How do we address the operands?• Register Only

• Immediate

• Base Addressing

• PC-Relative

• Pseudo Direct

Addressing Modes

Chapter 6 <106>

Register Only• Operands found in registers

– Example: add $s0, $t2, $t3

– Example: sub $t8, $s1, $0

Immediate• 16-bit immediate used as an operand

– Example: addi $s4, $t5, -73

– Example: ori $t3, $t7, 0xFF

Addressing Modes

Chapter 6 <107>

Base Addressing

• Address of operand is:base address + sign-extended immediate

– Example: lw $s4, 72($0)

• address = $0 + 72

– Example: sw $t2, -25($t1)

• address = $t1 - 25

Addressing Modes

Chapter 6 <108>

PC-Relative Addressing

0x10 beq $t0, $0, else

0x14 addi $v0, $0, 1

0x18 addi $sp, $sp, i

0x1C jr $ra

0x20 else: addi $a0, $a0, -1

0x24 jal factorial

beq $t0, $0, else

Assembly Code Field Values

4 8 0 3

op rs rt imm

6 bits 5 bits 5 bits 5 bits 5 bits 6 bits(beq $t0, $0, 3)

Addressing Modes

Chapter 6 <109>

Pseudo-direct Addressing

0x0040005C jal sum

...

0x004000A0 sum: add $v0, $a0, $a1

0000 0000 0100 0000 0000 0000 1010 0000JTA

26-bit addr (0x0100028)

(0x004000A0)

0000 0000 0100 0000 0000 0000 1010 0000

0 1 0 0 0 2 8

000011 00 0001 0000 0000 0000 0010 1000

op addr

Machine CodeField Values

3 0x0100028

6 bits 26 bits

(0x0C100028)

op imm

6 bits 26 bits

Addressing Modes

Chapter 6 <110>

Assembly Code

High Level Code

Compiler

Object File

Assembler

Executable

Linker

Memory

Loader

Object Files

Library Files

How to Compile & Run a Program

Chapter 6 <111>

• Graduated from Yale University with a Ph.D. in mathematics

• Developed first compiler

• Helped develop the COBOL programming language

• Highly awarded naval officer

• Received World War II Victory Medal and National Defense Service Medal, among others

Grace Hopper, 1906-1992

Chapter 6 <112>

• Instructions (also called text)

• Data

– Global/static: allocated before program begins

– Dynamic: allocated within program

• How big is memory?

– At most 232 = 4 gigabytes (4 GB)

– From address 0x00000000 to 0xFFFFFFFF

What is Stored in Memory?

Chapter 6 <113>

SegmentAddress

0xFFFFFFFC

0x80000000

0x7FFFFFFC

0x10010000

0x1000FFFC

0x10000000

0x0FFFFFFC

0x00400000

0x003FFFFC

0x00000000

Reserved

Stack

Heap

Static Data

Text

Reserved

Dynamic Data

MIPS Memory Map

Chapter 6 <114>

int f, g, y; // global variables

int main(void)

{

f = 2;

g = 3;

y = sum(f, g);

return y;

}

int sum(int a, int b) {

return (a + b);

}

Example Program: C Code

Chapter 6 <115>

int f, g, y; // global

int main(void)

{

f = 2;

g = 3;

y = sum(f, g);

return y;

}

int sum(int a, int b) {

return (a + b);

}

.data

f:

g:

y:

.text

main:

addi $sp, $sp, -4 # stack frame

sw $ra, 0($sp) # store $ra

addi $a0, $0, 2 # $a0 = 2

sw $a0, f # f = 2

addi $a1, $0, 3 # $a1 = 3

sw $a1, g # g = 3

jal sum # call sum

sw $v0, y # y = sum()

lw $ra, 0($sp) # restore $ra

addi $sp, $sp, 4 # restore $sp

jr $ra # return to OS

sum:

add $v0, $a0, $a1 # $v0 = a + b

jr $ra # return

Example Program: MIPS Assembly

Chapter 6 <116>

Symbol Address

Example Program: Symbol Table

Chapter 6 <117>

Symbol Address

f 0x10000000

g 0x10000004

y 0x10000008

main 0x00400000

sum 0x0040002C

Example Program: Symbol Table

Chapter 6 <118>

Executable file header Text Size Data Size

Text segment

Data segment

Address Instruction

Address Data

0x00400000

0x00400004

0x00400008

0x0040000C

0x00400010

0x00400014

0x00400018

0x0040001C

0x00400020

0x00400024

0x00400028

0x0040002C

0x00400030

addi $sp, $sp, -4

sw $ra, 0 ($sp)

addi $a0, $0, 2

sw $a0, 0x8000 ($gp)

addi $a1, $0, 3

sw $a1, 0x8004 ($gp)

jal 0x0040002C

sw $v0, 0x8008 ($gp)

lw $ra, 0 ($sp)

addi $sp, $sp, -4

jr $ra

add $v0, $a0, $a1

jr $ra

0x10000000

0x10000004

0x10000008

f

g

y

0xC (12 bytes)0x34 (52 bytes)

0x23BDFFFC

0xAFBF0000

0x20040002

0xAF848000

0x20050003

0xAF858004

0x0C10000B

0xAF828008

0x8FBF0000

0x23BD0004

0x03E00008

0x00851020

0x03E00008

Example Program: Executable

Chapter 6 <119>

y

g

f

0x03E00008

0x00851020

0x03E00008

0x23BD0004

0x8FBF0000

0xAF828008

0x0C10000B

0xAF858004

0x20050003

0xAF848000

0x20040002

0xAFBF0000

0x23BDFFFC

MemoryAddress

$sp = 0x7FFFFFFC0x7FFFFFFC

0x10010000

0x00400000

Stack

Heap

$gp = 0x10008000

PC = 0x00400000

0x10000000

Reserved

Reserved

Example Program: In Memory

Chapter 6 <120>

• Pseudoinstructions

• Exceptions

• Signed and unsigned instructions

• Floating-point instructions

Odds & Ends

Chapter 6 <121>

Pseudoinstruction MIPS Instructionsli $s0, 0x1234AA77 lui $s0, 0x1234

ori $s0, 0xAA77

clear $t0 add $t0, $0, $0

move $s1, $s2 add $s2, $s1, $0

nop sll $0, $0, 0

Pseudoinstructions

Chapter 6 <122>

• Unscheduled function call to exception

handler

• Caused by:

– Hardware, also called an interrupt, e.g., keyboard

– Software, also called traps, e.g., undefined instruction

• When exception occurs, the processor:

– Records the cause of the exception

– Jumps to exception handler (at instruction address

0x80000180)

– Returns to program

Exceptions

Chapter 6 <123>

• Not part of register file

– Cause: Records cause of exception

– EPC (Exception PC): Records PC where exception occurred

• EPC and Cause: part of Coprocessor 0

• Move from Coprocessor 0– mfc0 $t0, EPC

– Moves contents of EPC into $t0

Exception Registers

Chapter 6 <124>

Exception Cause

Hardware Interrupt 0x00000000

System Call 0x00000020

Breakpoint / Divide by 0 0x00000024

Undefined Instruction 0x00000028

Arithmetic Overflow 0x00000030

Exception Causes

Chapter 6 <125>

• Processor saves cause and exception PC in Cause

and EPC

• Processor jumps to exception handler (0x80000180)

• Exception handler:

– Saves registers on stack

– Reads Cause register

mfc0 $t0, Cause

– Handles exception

– Restores registers

– Returns to program

mfc0 $k0, EPC

jr $k0

Exception Flow

Chapter 6 <126>

• Addition and subtraction

• Multiplication and division

• Set less than

Signed & Unsigned Instructions

Chapter 6 <127>

• Signed: add, addi, sub

– Same operation as unsigned versions

– But processor takes exception on overflow

• Unsigned: addu, addiu, subu

– Doesn’t take exception on overflow

Note: addiu sign-extends the immediate

Addition & Subtraction

Chapter 6 <128>

• Signed: mult, div

• Unsigned: multu, divu

Multiplication & Division

Chapter 6 <129>

• Signed: slt, slti

• Unsigned: sltu, sltiu

Note: sltiu sign-extends the immediate before

comparing it to the register

Set Less Than

Chapter 6 <130>

• Signed:

– Sign-extends to create 32-bit value to load into

register

– Load halfword: lh

– Load byte: lb

• Unsigned:

– Zero-extends to create 32-bit value

– Load halfword unsigned: lhu

– Load byte: lbu

Loads

Chapter 6 <131>

• Floating-point coprocessor (Coprocessor 1)

• 32 32-bit floating-point registers ($f0-$f31)

• Double-precision values held in two floating

point registers

– e.g., $f0 and $f1, $f2 and $f3, etc.

– Double-precision floating point registers: $f0, $f2,

$f4, etc.

Floating-Point Instructions

Chapter 6 <132>

Name Register Number Usage

$fv0 - $fv1 0, 2 return values

$ft0 - $ft3 4, 6, 8, 10 temporary variables

$fa0 - $fa1 12, 14 Function arguments

$ft4 - $ft8 16, 18 temporary variables

$fs0 - $fs5 20, 22, 24, 26, 28, 30 saved variables

Floating-Point Instructions

Chapter 6 <133>

op cop ft fs fd funct


F-Type

• Opcode = 17 (0100012)

• Single-precision:– cop = 16 (0100002)

– add.s, sub.s, div.s, neg.s, abs.s, etc.

• Double-precision:– cop = 17 (0100012)

– add.d, sub.d, div.d, neg.d, abs.d, etc.

• 3 register operands:– fs, ft: source operands

– fd: destination operands

F-Type Instruction Format

Chapter 6 <134>

• Set/clear condition flag: fpcond

– Equality: c.seq.s, c.seq.d

– Less than: c.lt.s, c.lt.d

– Less than or equal: c.le.s, c.le.d

• Conditional branch

– bclf: branches if fpcond is FALSE

– bclt: branches if fpcond is TRUE

• Loads and stores

– lwc1: lwc1 $ft1, 42($s1)

– swc1: swc1 $fs2, 17($sp)

Floating-Point Branches

Chapter 6 <135>

Microarchitecture – building MIPS

processor in hardware

Bring colored pencils

Looking Ahead

Documents

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